NeurIPS paper gives RNNs provable state-estimation guarantees via control-theory observers
chriswolfvision · x · 2026-11-12
A NeurIPS 2026 paper by Andrieu, Bernard, Brivadis, Praly and Wolf, 'Provable State Estimation with Recurrent Models' (arXiv:2611.09217), provides the first formal convergence guarantees for RNN-based state estimation.
Approach
- Treats RNNs as time-discretized Neural ODEs and connects them to KKL observers from nonlinear control theory.
- If the latent dynamics are contracting and the system observable, a smooth injective map from the true physical state into latent space exists.
- Scaling a single gain κ drives estimation error exponentially toward zero; the paper bounds the MLP size needed to decode the latent state and extends guarantees to discrete residual RNNs.
Trade-off and experiments
- Higher κ makes the latent map harder to invert, requiring a larger MLP decoder.
- Validated on a real mobile robot over 27 km of navigation: the contracting GRU beats a vanilla GRU with substantially more stable training (mean ± std over 5 runs).
- Surprise finding: unconstrained GRUs converge to contracting dynamics on their own, suggesting contraction is an emergent property of well-trained sequence models.
Related event: NeurIPS Paper Delivers First Provable Guarantees for RNN State Estimation(2 posts)→
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